I was wondering that maybe he was preparing to shave.
If he was, then he didn't need shaving at Leduc's Barber Shop that morning. There is no testimony that he was there at Leducs, though 2 Fall River newspapers surmise this. However, the Evening Standard does not mention it, nor do the New York papers: Rochester & NYTimes.
If Andrew wasn't shaved, then his "Last Walk" (see Rebello, 565+), is flawed and so is the timeline.
If Andrew wasn't shaved, he may not have left the house as early as many think, because our first Witness to seeing him officially, is about 9:30 at The Union Savings Bank, Hart & Burrell.
The one thing we do know, which has no direct witness is that he mailed Lizzie's letter to Fairhaven at the post offce because it was returned.
We have 2 "gaps" in Andrew's timeline.
The one between 9 and 9:30 and another one between 9:55 and 10:20.
Either one of these is enough time for him to have killed Abby, believe it or not. Or to have been in the house when it happened...

*Trial
Bridget
Q. When Mr. Borden returned from letting Mr. Morse out where did he go, where did Mr. Borden go?
A. He came to the sink, and he cleaned his teeth in the sink, and after that he took a bowl, a big bowl, and filled it with water and took it up to his room.
Attached please see the timeline I prepared a while ago. It is from The Preliminary Hearing which not many of you have.